Convexity of coverings of projective varieties and vanishing theorems
| dc.creator | Bogomolov, F. | |
| dc.creator | De Oliveira, B. | |
| dc.date | 2004-05-04 | |
| dc.date.accessioned | 2026-07-07T05:07:56Z | |
| dc.date.available | 2026-07-07T05:07:56Z | |
| dc.description | This article is concerned with the convexity properties of universal covers of projective varieties. We study the relation between the convexity properties of the universal cover of X and the properties of the pullback map sending vector bundles on X to vector bundles on its universal cover. Our approach motivates a weakened version of the Shafarevich conjecture. We prove this conjecture for projective varieties X whose pullback map identifies a nontrivial extension of a negative vector bundle $V$ by the trivial line bundle with the trivial extension. We prove the following pivotal result: if a universal cover of a projective variety has no nonconstant holomorphic functions then the pullback map of vector bundles is almost an imbedding. Our methods also give a new proof of the vanishing of the first cohomology for negative vector bundles $V$ over a compact complex manifold $X$ whose rank is smaller than the dimension of X. | |
| dc.identifier | https://arxiv.org/abs/math/0405066 | |
| dc.identifier | http://arxiv.org/abs/math/0405066 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71059 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14F05; 32Q30; 32E05; 14E20 | |
| dc.title | Convexity of coverings of projective varieties and vanishing theorems | |
| dc.type | text |